What if you did a month on Oahu and a month on another island, like Maui? It would help to break it up a little bit and save on costs from island hopping, if that's something you're considering doing while there. Or even one month in the North Shore and one month in Kailua (for example), just to experience different parts of Oahu. My parents do VRBO/Airbnb rentals for the winter in Florida and stay in two different areas for one month each. They prefer one month rentals because its usually easier to find a place for just a month, and they're also not locked in for their full stay in Florida if they happen to not care much for the unit or the area after a while.
Are you considering the summer months because of kids and school? Otherwise, I would consider doing winter months to get out of potentially cold weather where you live. Hawaii can also be hot in the summer, and pretty busy with fellow summer vacationers.
IMO, I think it would be cost prohibitive to rent and live there for two months. When my parents go to Florida, they drive so they are not limited on what they can bring. They also have their car with them. Going to Hawaii, everything you bring will have to fit in your luggage, and you'd presumably have to do a long term car rental which adds to the cost. But, I do think it would be a fun and memorable experience, and if you have the finances and means to do it, then go for it! Its not a long term thing and you're not locked into anything beyond two months, so not a whole lot to lose. If you find yourselves homesick or antsy after a few weeks, then you know what your limit is for next time.
